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Optimizing Logical Execution Time Model for Both Determinism and Low Latency

Sen Wang, Dong Li, Ashrarul H. Sifat, Shao-Yu Huang, Xuanliang Deng, Changhee Jung, Ryan Williams, Haibo Zeng

TL;DR

The paper tackles the end-to-end latency and jitter challenges of the default LET model by optimizing the flexible LET (fLET) parameters. It introduces a novel abstraction of task communications using edge- and graph-level patterns (ELP/EFP and GLP/GFP) and develops LP-based, two-stage optimization with symbolic pruning to efficiently find near-optimal virtual offsets $O_i$ and virtual deadlines $D_i$ under schedulability constraints. The approach provides bounded suboptimality guarantees and supports multi-objective optimization of data age, reaction time, time disparity, and jitter, demonstrated on synthetic task sets and an autonomous-robot case study where fLET outperforms implicit communication, DBP, and prior LET extensions. The work significantly enhances fLET's practicality for real-time multicore systems by delivering deterministic timing with substantially improved end-to-end performance and scalable optimization techniques.

Abstract

The Logical Execution Time (LET) programming model has recently received considerable attention, particularly because of its timing and dataflow determinism. In LET, task computation appears always to take the same amount of time (called the task's LET interval), and the task reads (resp. writes) at the beginning (resp. end) of the interval. Compared to other communication mechanisms, such as implicit communication and Dynamic Buffer Protocol (DBP), LET performs worse on many metrics, such as end-to-end latency (including reaction time and data age) and time disparity jitter. Compared with the default LET setting, the flexible LET (fLET) model shrinks the LET interval while still guaranteeing schedulability by introducing the virtual offset to defer the read operation and using the virtual deadline to move up the write operation. Therefore, fLET has the potential to significantly improve the end-to-end timing performance while keeping the benefits of deterministic behavior on timing and dataflow. To fully realize the potential of fLET, we consider the problem of optimizing the assignments of its virtual offsets and deadlines. We propose new abstractions to describe the task communication pattern and new optimization algorithms to explore the solution space efficiently. The algorithms leverage the linearizability of communication patterns and utilize symbolic operations to achieve efficient optimization while providing a theoretical guarantee. The framework supports optimizing multiple performance metrics and guarantees bounded suboptimality when optimizing end-to-end latency. Experimental results show that our optimization algorithms improve upon the default LET and its existing extensions and significantly outperform implicit communication and DBP in terms of various metrics, such as end-to-end latency, time disparity, and its jitter.

Optimizing Logical Execution Time Model for Both Determinism and Low Latency

TL;DR

The paper tackles the end-to-end latency and jitter challenges of the default LET model by optimizing the flexible LET (fLET) parameters. It introduces a novel abstraction of task communications using edge- and graph-level patterns (ELP/EFP and GLP/GFP) and develops LP-based, two-stage optimization with symbolic pruning to efficiently find near-optimal virtual offsets and virtual deadlines under schedulability constraints. The approach provides bounded suboptimality guarantees and supports multi-objective optimization of data age, reaction time, time disparity, and jitter, demonstrated on synthetic task sets and an autonomous-robot case study where fLET outperforms implicit communication, DBP, and prior LET extensions. The work significantly enhances fLET's practicality for real-time multicore systems by delivering deterministic timing with substantially improved end-to-end performance and scalable optimization techniques.

Abstract

The Logical Execution Time (LET) programming model has recently received considerable attention, particularly because of its timing and dataflow determinism. In LET, task computation appears always to take the same amount of time (called the task's LET interval), and the task reads (resp. writes) at the beginning (resp. end) of the interval. Compared to other communication mechanisms, such as implicit communication and Dynamic Buffer Protocol (DBP), LET performs worse on many metrics, such as end-to-end latency (including reaction time and data age) and time disparity jitter. Compared with the default LET setting, the flexible LET (fLET) model shrinks the LET interval while still guaranteeing schedulability by introducing the virtual offset to defer the read operation and using the virtual deadline to move up the write operation. Therefore, fLET has the potential to significantly improve the end-to-end timing performance while keeping the benefits of deterministic behavior on timing and dataflow. To fully realize the potential of fLET, we consider the problem of optimizing the assignments of its virtual offsets and deadlines. We propose new abstractions to describe the task communication pattern and new optimization algorithms to explore the solution space efficiently. The algorithms leverage the linearizability of communication patterns and utilize symbolic operations to achieve efficient optimization while providing a theoretical guarantee. The framework supports optimizing multiple performance metrics and guarantees bounded suboptimality when optimizing end-to-end latency. Experimental results show that our optimization algorithms improve upon the default LET and its existing extensions and significantly outperform implicit communication and DBP in terms of various metrics, such as end-to-end latency, time disparity, and its jitter.
Paper Structure (39 sections, 16 theorems, 23 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 39 sections, 16 theorems, 23 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model and Definitions
  4. System Model
  5. Data Age and Reaction Time
  6. Time disparity
  7. Task Communication Mechanisms
  8. Problem Description
  9. fLET vs Alternative Communication Mechanism
  10. fLET Optimization Problem Descriptions
  11. Communication Patterns
  12. Motivation
  13. Edge Communication Patterns (ECP)
  14. Graph Communication Pattern (GCP)
  15. Evaluating Graph Communication Pattern
  16. ...and 24 more sections

Key Result

Lemma 1

Consider a feasible ELP of an edge $\tau_i \rightarrow \tau_j$ and two jobs $J_{j,q_u}$ and $J_{j,q_w}$ where $q_u < q_w$, their last-reading jobs specified by the ELP, $J_{i, \overleftarrow{q_u}}$ and $J_{i, \overleftarrow{q_w}}$, satisfy: $\overleftarrow{q_u} \leq \overleftarrow{q_w}$.

Figures (7)

  • Figure 1: The schedules of different communication protocols in Example \ref{['Example_setup']}. The upward and downward arrows represent job reading and writing times, respectively. Solid leftward arrows connect the longest immediate backward job chains, and dashed rightward arrows connect the longest immediate forward job chains. It is worth highlighting that fLET demonstrates superior performance compared to alternative methods after optimization. Figures \ref{['fig_fLET_Example']} and \ref{['fig_fLET_Example_sf_jitter']} serve merely as illustrations of the optimization results for different metrics. Importantly, our optimization approach supports the simultaneous optimization of multiple metrics.
  • Figure 2: Example DAG with two cause-effect chains.
  • Figure 3: A multi-graph with the edge last-reading patterns (ELPs) in Example \ref{['Example_setup']}. A complete graph last-reading pattern (GLP) comprises three ELPs from the three edges. There are $4\times 3 \times 3 = 36$ possible GLP combinations.
  • Figure 4: Communication pattern comparison. Consider a simple DAG with only one cause-effect chain $\tau_0 \rightarrow \tau_1$. Furthermore, to illustrate the idea more easily, we assume that $\tau_1$'s virtual deadline is locked at 20. In this case, the optimal edge last-reading pattern (ELP) is $\boldsymbol{ELP}_{E_0}(2)$: $\boldsymbol{ELP}_{E_0}(3)$ is infeasible; $\boldsymbol{ELP}_{E_0}(2)$ has shorter end-to-end latency than $\boldsymbol{ELP}_{E_0}(1)$ and $\boldsymbol{ELP}_{E_0}(0)$ ($\boldsymbol{ELP}_{E_0}(0)$ and $\boldsymbol{ELP}_{E_0}(1)$ require moving $\tau_1$'s virtual offset forward). Notice that we can find the optimal ELP based on the pattern index with a feasibility check (a larger index implies a shorter immediate backward job chain).
  • Figure 5: Relative performance gap and runtime (log scale) when optimizing different performance metrics individually. fLET outperforms other communication protocols and state-of-the-art optimization algorithms while offering broader applicability.
  • ...and 2 more figures

Theorems & Definitions (64)

  • Definition 3.1: Job chain Gnzel2021TimingAO
  • Definition 3.2: Length of a job chain, $\text{Len}(\mathcal{C}^J)$
  • Definition 3.3: Last-reading job
  • Definition 3.4: Immediate backward job chain, Gnzel2021TimingAO
  • Definition 3.5: First-reacting job
  • Definition 3.6: Immediate forward job chain, Gnzel2021TimingAO
  • Example 1
  • Definition 3.7: Time disparity, Percept21_RTSS
  • Example 2
  • Definition 4.1: Virtual offset, $O_i$
  • ...and 54 more